Chapter 1 Tutorial 2

In an economy where a unit of labour can produce either 1 unit of x or 4 units of y (or any linear combination of the two) and a unit of capital can produce either 4 units of x or 1 unit of y (or any linear combination of the two). There are 100 units of each means of production. Suppose now that the discovery of new production technologies allowed the production of both x and y by using only one of the two means of production (without a change in their respective productivity).
a) What will be the production possibility curve?
b) What will now be the opportunity cost of producing 50 units of x?
c) Will it change if we produced 90 units of x?

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16 Comments

  1. sherlikaa says:

    Hi Quickienomics, So it is like the imaginary lines show us that it is actually the max production for both X and Y and then because of the new technology, it can produce both X and Y so it will be an additional 100 X and 100Y to show that now the PPC is now higher but the shape of the PPC remains the same? is it correct? Thank you for your Video . 🙂

  2. Matt says:

    Hi,
    Can I ask what exactly is the reason why for the remaining 100y we have to use the capital constraint, or using the labour constraint for the remaining 100x?

    Thanks.

    • Matt says:

      Is the reason because, since we’re using the cheaper constraint, (eg labour), to produce the 400y (since it’s more efficient), we’re only left with the other constraint (capital) to produce the remaining 100y?

  3. hy says:

    Hi can I ask for this qn, do we need to label the slope of the new ppf? will marks be deducted if we never label? 🙂

    • Quickienomics says:

      Hi!

      It will definitely be more pleasant to look at if you labelled the new PPF. It gives off a better impression on your answer script! 🙂

  4. hy says:

    Is it correct if I write L: x + quarter of y not more than equal to 100 on the new L constraint?

    Can u adivce? 🙂

    Btw, I wonder if u had read before qn 3 from the study guide and amos’s tb? Robinson bake 10 bread or peel 20 potatoes. Friday bake 5 bread or peel 30 potatoes. if they believe in equality in consumption, would they specialise and trade?

    is it enough if I follow ur steps of answering specialisation and trade qns and apply on qn 3?
    Meaning: Draw original ppf, find opp cost, see which has lower opp cost result in comp adv result in specialise, then find intl price, finally draw the trade benefits (new consumption possibility)? The answer in the study guide further explain on what if they want to be better off from a material point of view as well as peruse other values like equality, the distribution which they shld aim for is 5 loaves of bread and 15 potatoes each. hence the price of a loaf of bread is 3 potAtoes and the price of a single potato is one third of a loaf of bread. how do the author derive that?. The book nv state the intl price at all. and their new
    consumption possibility diagram only include the orginal ppf plus the equality in consumption part.

    I found out myself tt the intl price is 4 potatoes per loaf of bread or a quarter loaf of bread per potato. so for robinson’s new consumption possibility, I will use 4 x 10=40. I will draw a new line from orginal y axis = 10 to new point x=40.

    am I correct?

    sorry for this lengthy comment. I hope u can clarify my doubts : greatly appreciate!

    • Quickienomics says:

      Hi, the L constraint is actually 1x + 1/4y less than equal to 100. 🙂

      In his textbook, he is going beyond the question by talking about equality, which I think is good because it makes the answer very vibrant and substantial. You see, we can choose the intl price to be any value between the 2 opportunity costs as described in the video right? So he has chosen a price that ensures both of them have got equal consumption. So that price happens to be 4. Equal consumption means that both of them will get to eat the same number of bread and potatoes. Fair right? lol

      And yes you are right regarding drawing the new lines. Not bad! Keep it up!

  5. hy says:

    Thank you thank you thank you! 🙂

    It’s the crucial period now!!! Haha

  6. Dawn says:

    1) The production of a unit of x requires 1/2 a unit of labour and 1 unit of capital. To produce a unit of y one would need 1 unit of labour and 1/2 a unit of capital.

    2)One unit of labor can produce either 2 units of x or 1 unit of y. One unit of captial can produce either 1 unit of x or 2 units of y. There are 100 units of capital and 100 units of labor.

    So my question is how do you actually work out the above resource constraint? It’s not as straight forward as the one in above example. Do you mind show me the step? Appreciated!

    • Quickienomics says:

      Hi, I believe you just emailed me. I have replied your email.

      For the benefit of others, here’s my reply:

      “1) The production of a unit of x requires 1/2 a unit of labour and 1 unit of capital. To produce a unit of y one would need 1 unit of labour and 1/2 a unit of capital.

      2) 1/4 a unit of labour and 1/2 a unit of capital will produce one unit of x; 1/2 a unit of labour and 1/4 a unit of capital will produce a unit of y. There are 100 units of capital and 100 units of labour.”

      For question 1 you will need the total amount of labour and capital if you want to form the constraint equation.

      For question 2, simple identify what can 1 unit of capital and 1 unit of labour produce first.

      1 unit of labour produces 4x or 2y. (Workings: If 1/4L = 1x, 1L = 4x. If 1/2L = 1y, 1L = 2y)
      1 unit of capital produces 2x or 4y. (Workings: If 1/2K = 1x, 1K = 2x. If 1/4K = 1y, 1K = 4y)

      With that, just flip the figures upside down like demonstrated in my videos:
      Labour Constraint Equation: 1/4x + 1/2y = 100
      Capital Constraint Equation: 1/2x +1/4y =100

      To check the validity of the equations, use this example: I will produce only x using all my capital. I should be able to produce 200x using 100K. Substituting x=200 and y=0 into the Capital Constraint equation will give me 100, which is same as the figure on the right hand side.

      From there, just isolate Y on the left side to get your regular Y=mX + c form to draw your constraints on the graph.

  7. TCR says:

    what would be the equation if given that 1 k gives you 3y or 3x and the value of k available is 50